In a multi-participant modeled virtual reality environment, avatars are modeled beings that include moveable eyes creating the impression of an apparent gaze direction. Control of eye movement may be performed autonomously using software to select and prioritize targets in a visual field. Sequence and duration of apparent gaze may then be controlled using automatically determined priorities. Optionally, user preferences for object characteristics may be factored into determining priority of apparent gaze. Resulting modeled avatars are rendered on client displays to provide more lifelike and interesting avatar depictions with shifting gaze directions.